
def a__       (			A_,	A_   ):






  '''simple docstring'''





  __magic_name__								=			1  # To kept the Calculated Value
  # Since C(n, k) = C(n, n-k)
  if k > (n - k):
    __magic_name__								=			n - k
  # Calculate C(n,k)
  for i in range(A_   ):
    result *= n - i
    result //= i + 1
  return result

def a__       (			A_   ):






  '''simple docstring'''





  return binomial_coefficient(2 * node_count,	A_   ) // (node_count + 1)

def a__       (			A_   ):






  '''simple docstring'''





  if n < 0:
    raise ValueError("""factorial() not defined for negative values"""   )
  __magic_name__								=			1
  for i in range(1,	n + 1   ):
    result *= i
  return result

def a__       (			A_   ):






  '''simple docstring'''





  return catalan_number(A_   ) * factorial(A_   )


if __name__ == "__main__":
    __lowerCAmelCase     :	Union[str, Any]       			=  int(input('Enter the number of nodes: ').strip() or 0)
    if node_count <= 0:
        raise ValueError('We need some nodes to work with.')
    print(
        F'''Given {node_count} nodes, there are {binary_tree_count(node_count)} '''
        F'''binary trees and {catalan_number(node_count)} binary search trees.'''
    )



# Copyright 2023 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__lowerCAmelCase     :	Tuple       			=  {'configuration_timm_backbone': ['TimmBackboneConfig']}


try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __lowerCAmelCase     :	str       			=  ['TimmBackbone']


if TYPE_CHECKING:
    from .configuration_timm_backbone import TimmBackboneConfig

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_timm_backbone import TimmBackbone

else:
    import sys

    __lowerCAmelCase     :	str       			=  _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)

